Classical Theory of Electricity and Magnetism: A Course of Lectures (Texts and Readings in Physical Sciences Book 21)

This book examines the topics of magnetohydrodynamics and plasma oscillations, in addition to the standard topics discussed to cover courses in electromagnestism, electrodynamics, and fundamentals of physics, to name a few. This textbook on electricity and magnetism is primarily targeted at graduate students of physics. The undergraduate students of physics also find the treatment of the subject useful. The treatment of the special theory of relativity clearly emphasises the Lorentz covariance of Maxwell's equations. The rather abstruse topic of radiation reaction is covered at an elementary level, and the Wheeler–Feynman absorber theory has been dwelt upon briefly in the book. Foreword to the Revised Edition 6 Preface 8 Contents 9 About the Author 13 1 Empirical Basis of Electrostatics 14 1.1 The Idea of Electric Charge 14 1.2 The Law of Interaction of Point Charges 14 2 Direct Calculation of Field in Some Cases 20 2.1 Interaction Between Dipoles 21 2.2 Potential due to Surface Distribution of Charges and Dipoles 22 2.3 The Dirac δ-Function 26 3 Gauss' Theorem, Laplace and Poisson Equations 30 3.1 Equations of Laplace and Poisson 32 3.1.1 Green's Theorem in Vector Calculus 34 3.1.2 A Formula of Interest in Field Theory 34 3.1.3 Earnshaw's Theorem 35 4 Analysis of the Electrostatic Field: Multipole Moments 37 4.1 Energy of Multipoles in an External Field 43 5 Dielectrics and the Uniqueness Theorem 45 5.1 Boundary Conditions to be Satisfied at the Interface of Two Different Dielectrics 47 5.2 The Uniqueness Theorem 49 5.3 Field in a Cavity in a Dielectric 53 5.4 Molecular Polarizability and Clausius-Mossotti Relation 54 6 Solution of the Laplace Equation 59 6.1 Rectangular Cartesian Coordinates 59 6.2 Cylindrical Polar Coordinates 60 6.3 Method of Electrical Images 62 6.3.1 A Point Charge in Front of an Infinite Conducting Plane 62 6.3.2 Conducting Sphere 64 6.3.3 Two Spheres Intersecting at Right Angle 66 6.4 Green's Function Method 67 6.5 Method Using Complex Variables 71 7 Field Energy and Forces in Electrostatics 76 7.1 Electrostriction 86 7.2 Pressure Discontinuity at the Boundary of a Dielectric 87 7.3 Force Sucking in a Dielectric into a Capacitor 88 7.4 Force on the Surface of a Charged Conductor 90 8 Stationary Currents and Magnetic Fields 92 8.1 Magnetic Moment or a Current Distribution 96 8.2 Relation Between Magnetic Moment and Angular Momentum for a Classical System 98 8.2.1 Larmor Precession 98 8.3 Permanent Magnets and the Vector H 99 8.4 Boundary Conditions at the Interface of Two Media 104 8.5 Scalar and Vector Potentials for a Static Magnetic Field 104 8.6 Uniformly Magnetized Sphere 106 9 Electromagnetic Induction and Energy of the Magnetic Field 109 9.1 Law of Induction in a Moving Coil or Medium 110 9.2 Energy of the Magnetostatic Field 112 9.3 Calculation of Self and Mutual Inductances 116 9.4 Current in Circuits with Inductance, Resistance and Capacitance 119 9.4.1 The Case of an Alternating Impressed Electromotive Force 120 10 Maxwell's Equations, Electromagnetic Energy and Momentum 123 10.1 The Electromagnetic Waves in an Isotropic Homogeneous Dielectric 126 10.2 Energy Flux and the Poynting Vector 128 10.3 The General Stress Tensor and Momentum of Radiation 129 10.4 The Pressure of Radiation 130 11 Reflection and Refraction of Electromagnetic Waves 133 11.1 Total Internal Reflection 139 11.2 Reflection at Conducting Surfaces (Metallic Reflection) 141 12 Wave Guides and Cavity Resonators 147 12.1 Transverse Electromagnetic Waves (TEM Waves) 150 12.2 TM and TE Modes 151 12.3 Energy Flux, Attenuation in Wave Guides and Q of Cavities 152 12.3.1 Rectangular Transverse Section 155 12.3.2 Circular Cylindrical Cavity 157 13 Electromagnetic Waves in Anisotropic Media 160 13.1 The Relation Between the Directions of D, B, k, etc. 162 13.2 The Relation Between the Vectors in the Two Waves with the Same Wave Normal 163 13.3 Crystal Classes and Optic Axes 165 13.4 Conical Refraction 166 13.5 External Conical Refraction 168 14 Solution of Maxwell's Equations: Retarded and Advanced Potentials 171 14.1 The Near Field and the Far Field 176 15 Analysis of the Radiation Field 180 15.1 The Hertz Vector and Hertz's Method of Analysis 186 16 Field Due to a Moving Charged Particle 192 16.1 Field of a Particle in Uniform Rectilinear Motion 194 16.2 The Method of Virtual Quanta 198 16.3 Number of Equivalent Photons in the Virtual Radiation Field 200 17 Field of a Particle in Non-Uniform Motion 204 17.1 Radiation from a Particle Describing a Circular Orbit with Uniform Velocity—Acceleration Always Orthogonal to the Velocity 208 17.2 Classical Theory of Bremsstrahlung 210 18 Electrons in Material Media 216 18.1 Cerenkov Radiation 216 18.2 Scattering of Electromagnetic Waves by Electrons 220 18.3 Dispersion and Absorption 224 19 Motion of Charged Particles in Electromagnetic Fields 228 19.1 Weak Perturbations and Drift of the Guiding Centre 235 19.2 Slow Temporal Variation of Magnetic Field—Adiabatic Invariants 241 19.3 Confinement of Charged Particles in Non-homogeneous Magnetic Fields—The Magnetic Bottle and Magnetic Mirror 242 20 Magnetohydrodynamics—Conducting Fluids and Magnetic Fields 245 20.1 Stationary Solutions of the Magneto-Hydrodynamic Equations 248 20.2 The Pinch Effect 251 20.3 Instability of the Cylindrical Plasma 253 20.4 The Magneto-Hydrodynamic Waves 254 20.5 Dissipative Effects 258 21 Two Component Plasma Oscillations 260 21.1 Waves in the Plasma 263 22 The Theory of the Electron 269 22.1 Critique of the Classical Theory 273 22.2 The Radiation Reaction 274 22.3 The Wheeler–Feynmann Absorber Theory of the Radiation Reaction 275 23 Special Theory of Relativity and Electromagnetism 277 23.1 The Lorentz Transformation Formulae 278 23.2 Covariant and Contravariant Vectors and Tensors 281 23.3 Variation of Mass with Velocity 285 23.4 Tensor Form of the Equation of Electromagnetism 287 24 Variational Principle Formulation of Maxwell's Equations and Lagrangian Dynamics of Charged Particles in Electromagnetic Fields 294 24.1 Lagrangian and Hamiltonian of a Charged Particle in an Electromagnetic Field 297 Appendix A Index 299 Index 299